Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

TL;DR

This paper derives a formula for low-lying energy levels in quantum spin systems, clarifies the conditions for quenching of macroscopic quantum coherence, and introduces the concept of macroscopic Fermi-particles with explicit tunneling rate calculations.

Contribution

It provides a new formula for energy levels, clarifies the quenching mechanism of macroscopic quantum coherence, and introduces the concept of macroscopic Fermi-particles.

Findings

Low-lying levels follow a specific cosine-dependent formula.

Quenching of coherence occurs when cos(s+ξ)π vanishes.

Tunneling rate remains finite for all spin values, including integer and half-integer.

Abstract

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = \epsilon_0 - 2\triangle\epsilon cos (s+\xi)\pi$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+\xi)\pi$ in disagreement with the suppression of tunneling (i.e. $\triangle\epsilon = 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangle\epsilon)/(\pi)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.